Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes

TL;DR

This paper develops new criteria for symplectic self-orthogonality in quasi-cyclic codes and constructs quantum codes with record-breaking parameters using these conditions.

Contribution

It introduces novel necessary and sufficient conditions for symplectic self-orthogonality in one- and two-generator quasi-cyclic codes and applies them to create improved quantum codes.

Findings

New criteria for symplectic self-orthogonality

Construction of quantum codes with record-breaking parameters

Improved bounds on quantum code performance

Abstract

This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both matrix and polynomial approaches. We provide two versions of necessary and sufficient conditions for two-generator quasi-cyclic codes for symplectic self-orthogonality and the symplectic dual-containing condition. Additionally, using these necessary and sufficient conditions, we construct new quantum codes with record-breaking parameters that improve upon current records.